In practice the finite RS-independent physical observables at NLO and beyond are usually computed
as combinations of separate, in general UV and/or IR divergent contributions living in different
partonic phase spaces. (UV renormalization is understood in what follows.)
To render individual contributions from each partonic phase space IR-finite and RS-independent respectively,
one can add and subtract properly defined auxiliary IR-subtraction terms.
The introduction of these auxiliary terms are designed to ensure the cancellation of all intermediate
IR-divergences of amplitudes in each partonic phase space, while on the other hand
they leave no trace in the final properly combined physical observables.
This is the idea of IR-subtraction methods [1]}, [2]},
which are nowadays available in many different versions (e.g., [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}).
